Question

the value of 'g' at a distance of 2R (where R is the radius of the earth) from the centre of the Earth is​

Answer 1

Answer:

Explanation:

he easiest way to calculate would be to get it in ratios. Let's say g is the acceleration due to gravity on the surface of the earth where the radius is R, and g' is the acceleration due to gravity at a distance of 2R away from the earth's center. (Will address the question’s 2R from the surface making 3R from the center at the end). We know that on the surface of the earth the g value is 9.81m/s^2. The equation for g is as follows : g = GM/R^2, and for g' = GM/(2R)^2. Then let's set up the equation ratio as appears below : g'/g = R^2/(2R)^2 as GM cancels out, and entities with R flip vertically in the expression. So you have g'/g = R^2/4R^2 = 1/4, hence g' = (1/4)g which will give you g' = (1/4)(9.81m/s^2) = 2.453m/s^2. For the question the distance is actually 3R from the center of the earth hence the g” value will be 1/9•g which is 1.09m/s^2. Now all this I could have done in my head and given you the answer in one line, but then it will not demonstrate the simple mathematical beauty of it all… The longer way to do it would be to get the values of G, R, and M, and then perform the calculation which will give you the same answer ! The ratio bypasses the longer more elaborate calculation pathway…